>I mean, until medicine becomes perfect, then is sickness an any more unreasonable cause of death than old age?

Yes, of course. It's much better to die peacefully and in full possession of one's self than of wasting sickness or mental degeneration.

As in, several people in my family have living wills to this effect, that kind of better.

>Perfect medicine would also cure death from old age, right?

Once again: yes, of course. But we're nowhere near there yet, so what we can do is make sure people can die without suffering overmuch.